The sum of two numbers is $49$, and their difference is $21$. What are the two numbers?
Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 49}$ ${x-y = 21}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 70 $ $ x = \dfrac{70}{2} $ ${x = 35}$ Now that you know ${x = 35}$ , plug it back into $ {x+y = 49}$ to find $y$ ${(35)}{ + y = 49}$ ${y = 14}$ You can also plug ${x = 35}$ into $ {x-y = 21}$ and get the same answer for $y$ ${(35)}{ - y = 21}$ ${y = 14}$ Therefore, the larger number is $35$, and the smaller number is $14$.